Chapter 3 SMITH CHART Outlines - PDF

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Chapter 3 SMITH CHART Outlines - PDF Powered By Docstoc
					               Chapter 3
            SMITH CHART




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Outlines
  Construction of Smith Chart
  Operations and Applications of Smith Chart




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SMITH CHART:

  By P. H. Smith in 1939

  A graphical tool for the calculation of impedance
  and reflection coefficient

  A useful tool of visualizing the concepts and
  procedures of RF circuit designs

  http://www.sss-mag.com/smith.html

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 Construction of Smith Chart

                                                       lossless TL : Z 0 : real,   γ = jβ
     Γin             Z0 , β          ΓL       ZL
                                                              Z − Z0   Z −1
                                                        Γ =          =
           Z in                      Z in = Z L               Z + Z0   Z +1


      let         Γ = Γ r + jΓ i ,    Z = Z / Z 0 = r + jx

                                                        2                2
                                               r            1 
           equation for resistance r :  Γ r −       + Γi = 
                                                         2
                                                                   
                                              1+ r         1+ r 

                                                                    2
                                                                1   1
                                            (Γ r   − 1) +  Γ i −  = 2
                                                       2
           equation for reactance x :
                                                                x  x


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for passive load : | Γ |≤ 1,    r :0 ~ ∞,     x : −∞ ~ 0 ~ ∞

  | Γ |≤ 1         Γ within the unit circle
                                                              £F   i
                   centered at the origin
                                                                   (0, 1)

              2                 2
        r            1 
  Γr −       + Γi = 
                  2
                            
       1+ r         1+ r                     x = 0.3               x=1

                                                                                 x=2
     resistance circles:
                                  1                                                             (1, 0)
      center ( r , 0) , radius =
              1+ r               1+ r          x=0                                               £F
                                                                               r=2                    r

                            2                                               r=1
                      1   1
  (Γ r   − 1) +  Γ i −  = 2
             2

                      x  x                                           r = 0.5
                                                       r=0         x = -1
     reactance circles:
                                 1                                                 £F       =1
      center (1, 1 ) , radius =                                                         r
                 x              |x|                          Γ plane

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  Smith Chart




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    Important Notes on Smith Chart
             r = 0, pure reactance
                                                                        r=1

                                            r < 1 : R < Z0


                            x > 0 : inductive
    Γ = −1, SC                                     r > 1 : R > Z0             Γ = 1, OC



                            x > 0 : capacitive                                Γ = 0, matched
x = 0, pure resistance




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  Basic Information by Smith Chart
       P                                               x

                                                                              φ
   Γ          Z0            ZL
                                                                        P

       Z
                                                                    r

  Γ =| Γ | e jφ
 Z = Z0 ( r + jx)


                                                                              |Γ|,
                                                                              VSWR,
                                                                              RL



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Admittance Smith Chart

      Y Z0 1 1 − Γ
 y=     = = =      = g + jb
      Y0 Z z 1 + Γ




                    Admittance Smith Chart


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ZY Smith Chart




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Finding Impedance and Admittance

                               1.0                                 by Z Smith Chart :
                                                 0.5                       zP = 1 + j
                                                                           yP = 0.5 − j0.5


                                       P
                                                                   by Y Smith Chart :
                                                                           yP = 0.5 − j0.5
                     0.5         1.0       0.5




             0.5




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Finding z, y, Γ Along Transmission Line
                                                d
      Q                  P                    ar tor
                                           tow nera
                                             ge
ΓQ                 ΓP          ZL
                                                                                  k
                                                                     P

     ZQ                 ZP                                                              = kλ

      = kλ                                                           Q

     ΓQ = Γ Pe− j2β
                                              to
                    − j 4 kπ               lo wa
          = Γ Pe                             ad rd


          Rotating 360 degree ⇒ = 0.5λ
          Quarter wavelength transformer:              = λ /4   zQ = 1/ zP = yP

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Example

 Determine the length of a 50 Ohm open-circuited transmission
 line shown in figure so that the input impedance is Z IN (l ) = j100Ω




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 Series Element




                            series connect

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 Shunt Element




                 shunt connect

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Example




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Example




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Example




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Example




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Practice :

   A 50Ω lossless transmission line is terminated by a
 100 Ω resistor in series with a 2 nH inductor. The
 electrical length of the line is 270° at 2.4 GHz. Plot Zin
 and Γin verse frequency in Smith chart for f = 1.2 to 3.6
 GHz by ADS. Find the Zin and Γin of the RL-terminated
 transmission line at f = 3.2GHz.




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